Theorems · Theorem · number theory
NumberField.InfinitePlace.norm_embedding_of_isReal
∀ {K : Type u_1} [inst : Field K] {w : NumberField.InfinitePlace K} (hw : w.IsReal) (x : K),
‖(NumberField.InfinitePlace.embedding_of_isReal hw) x‖ = w x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Complexproof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- NumberField.InfinitePlacestatement and proof · cited by 604
- NumberField.InfinitePlace.IsRealstatement and proof · cited by 301
- Complex.norm_realproof · cited by 105
- NumberField.InfinitePlace.embedding_of_isRealstatement and proof · cited by 12
- NumberField.InfinitePlace.norm_embedding_eqproof · cited by 10
- NumberField.InfinitePlace.embedding_of_isReal_applyproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.normAtPlace_applyproof · cited by 8
- NumberField.InfinitePlace.isometry_embedding_of_isRealproof · cited by 2